Topology and Advanced Analysis (G1026)

15 credits, Level 6

Autumn teaching

This module will introduce you to some of the basic concepts and properties of topological spaces. The subject of topology has a central role in all of Mathematics and having a proper understanding of its concepts and main theorem is essential as part of an undergraduate mathematics curriculum.

Topics that will be covered in this module include:

  • topological spaces
  • base and sub-base
  • separation axioms
  • continuity
  • metrisability
  • completeness
  • compactness and coverings
  • total boundedness
  • Lebesgue numbers and Epsilon-nets
  • sequential compactness
  • Arzela-Ascoli Theorem
  • Montel's theorem
  • infinite products
  • box and product topologies
  • Tychonov Theorem. 

Teaching

100%: Lecture

Assessment

20%: Coursework (Problem Set)
80%: Examination (Unseen examination)

Contact hours and workload

We’re currently reviewing contact hours for modules and will update with further information as soon as it is available.

This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.

Courses

This module is offered on the following courses: